There have long been quiet but persistent complaints of discrimination against women fashion designers in the NY-Paris-Milan world of haute couture. This 2005 NYT article lays out the evidence than an Old Boys Club of male designers discriminates against women.
We can test whether women are as discriminated against in the parallel but separate world of designing clothes for movies by looking at Wikipedia's lists of Oscar nominees. Best Costume Design nominations generally go for work on period films or fantasy films aimed at girls. For example, the current nominees are three 19th Century period films — Lincoln, Anna Karenina, and Les Miserables versus two versions of Snow White: Mirror, Mirror and Snow White and the Huntsman.
So, Costume Design Nominations aren't an apples-to-apples direct test of the sense of where fashion is headed next fall, like haute couture designers attempt to do. Instead, Hollywood honorees are designed for accurate and exquisite reproductions of past fashions, usually with some attempt to make them accessible to current tastes. Thus, Hollywood's top costume designers are conservative restorationists, rather than on the fashion forward cutting edge like the Old Boys Club of New York design. Still, these Oscar nominations allow a sort of oranges and tangerines comparison.
The Best Costume Design award was invented in 1948, and Edith Head quickly emerged as the most honored designer, garnering 35 nominations and 8 Oscars. Over the last ten years, women have earned 80% of nominations.
So, designing clothes for Hollywood is much less male-dominated than designing clothes for the runway.